Algebra 1 Practice - Write an Equation in Slope-Intercept Form (Example 2)

Sure, here's how to write an equation in slope-intercept form directly, given information about the slope, points, or y-intercepts:

### 1. **Using Slope and Y-Intercept**

If you have the slope \( m \) and the y-intercept \( b \), you can directly write the equation in slope-intercept form:

\[ y = mx + b \]

**Example:**
- Slope (\( m \)) = 3
- Y-intercept (\( b \)) = -2

The equation is:

\[ y = 3x - 2 \]

### 2. **Using a Point and the Slope**

If you have the slope \( m \) and a point \((x_1, y_1)\), you can find the y-intercept \( b \) and then write the equation in slope-intercept form.

1. **Calculate the y-intercept \( b \):**

Rearrange the slope-intercept form \( y = mx + b \) to solve for \( b \):

\[ b = y - mx \]

Substitute the coordinates of the point \((x_1, y_1)\) and the given slope \( m \):

\[ b = y_1 - m x_1 \]

2. **Write the equation:**

Substitute the slope \( m \) and y-intercept \( b \) into the slope-intercept form:

\[ y = mx + b \]

**Example:**
- Slope (\( m \)) = 4
- Point = (2, 5)

Calculate \( b \):

\[ b = 5 - 4 \cdot 2 \]
\[ b = 5 - 8 \]
\[ b = -3 \]

The equation is:

\[ y = 4x - 3 \]

### 3. **Using Two Points**

If you have two points \((x_1, y_1)\) and \((x_2, y_2)\), follow these steps:

1. **Calculate the slope \( m \):**

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

2. **Find the y-intercept \( b \):**

Substitute one of the points and the slope into the equation \( y = mx + b \) to solve for \( b \):

\[ b = y - mx \]

Use one of the given points \((x_1, y_1)\):

\[ b = y_1 - m x_1 \]

3. **Write the equation:**

Substitute the slope \( m \) and y-intercept \( b \) into the slope-intercept form:

\[ y = mx + b \]

**Example:**
- Points = (1, 3) and (4, 11)

Calculate the slope \( m \):

\[ m = \frac{11 - 3}{4 - 1} = \frac{8}{3} \]

Find the y-intercept \( b \):

\[ b = 3 - \frac{8}{3} \cdot 1 \]
\[ b = 3 - \frac{8}{3} \]
\[ b = \frac{9}{3} - \frac{8}{3} \]
\[ b = \frac{1}{3} \]

The equation is:

\[ y = \frac{8}{3}x + \frac{1}{3} \]

Using these methods, you can determine the slope-intercept form of a linear equation given the necessary information.

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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa

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